Численное моделирование процесса фильтрации газа в многослойных пористых средах
Аннотация
Рассматривается математическая модель, методы и алгоритмы численного решения задач фильтрации газа в двух пластовых пористых средах c наличием слабопроницаемой перемычки. Нижний пласт разрабатывается системой нескольких батарей скважин с различными дебитами. Математическая модель процесса нестационарной фильтрации газа в пористой среде описана системы нелинейными дифференциальными уравнениями параболического типа. При численном решении краевой задачи используется метод прогонки для систем конечно-разностных уравнений. Система конечно-разностных уравнений относительно функции давлений нелинейно, поэтому для ее применяется итерационный метод, основанный на методике квазилинеаризации нелинейных членов. Разработаны вычислительные алгоритмы и программного обеспечения для проведения вычислительных экспериментов по исследованию нестационарных процессов фильтрации газа в двух пластовых пористых средах. Приведены результаты работы разработанного программного обеспечения и все результаты вычислительных экспериментов представлены в графическом виде.
Маколада суст утказувчан кат лам билан богланганикки катламли Foeak мухитда газнинг фильтрланиш масаласи математик модели, уни ечишнинг сонли усули ва алгоритми келтирилган.Пастки катлам бир неча турли дебитли кудуклар тизимидан ташкил топган холда ишлайди. Faвaк мухитда газнинг ностационар фильтрланиш жараёни математик модели чизиксиз бир бири билан богланган параболик типли дифференциал тенгламалар тизимибилан ёзилади. Чегаравий масалани сонли ечишда чекли айирмалар тизими учун прогонка усули кулланилада.Чекли айирмалар тизими босим функцияларига нисбатан чизиксиз булгани сабаб, квазилинеаризация усули кулланилиб квазичик тенгламалар тизимига келтирилади. Икки катламли гавак мухитда газларнинг фильтрланиш жараёнини тадкик килиш учун хисоблаш тажрибаларини утказиш максадида масалани ечиш алгоритми ва дастурий таъминот ишлаб чикилган. Дастурий таъминотнинг ишлаши натижалари ва барча хисоблаш тажрибалари натижалари график холда келтирилган.
Modern computer technology creates the opportunity on a qualitatively new basis to solve the problems of designing rational development of gas fields. Modern PCs allow you to take into account, at the stages of designing and analyzing the development of natural gas fields, a variety of natural factors. This, in turn, significantly increases the reliability of the resulting solutions of geological, gas-hydrodynamic and technical-economic problems.When considering issues related to the design, analysis and regulation of the development of multi-layer deposits of natural gases, it is necessary to investigate a large number of options on the PC. Here, the application of methods of mathematical modeling and the theory of computational experiment may prove to be effective. As a result of the computational experiment on a PC, the number of variants under study is substantially reduced.Many problems that have to be solved in the design, analysis and determination of the prospects for the development of gas and gas condensate fields are reduced to the integration of nonlinear differential equations of parabolic type. The necessity to take into account a great variety of geological factors leads to a significant complication of the original differential equations. Often the complexity of differential equations and boundary conditions reaches such a degree that the problems of greatest practical interest can not be solved in analytical form. Therefore, mathematical modeling is increasingly used for such calculations. The application of mathematical modeling for solving problems of underground gas hydrodynamics is based on the mathematical analogy of the flow of filtration processes.The article deals with the mathematical model, methods and algorithms for numerical solution of gas filtration problems in two-porous porous media with the presence of a weakly permeable bridge. In this case, filtration problems are considered two-dimensional and analytical solutions are constructed for certain schematized filtration flows. In addition, information on reservoir properties of the seams necessary for this class of problems has been made much easier. The presence of a gasdynamic connection between the layers is taken into account by the corresponding recording of the differential equations of unsteady gas filtration. A mathematical model of the process of nonstationary gas filtration in a porous medium is described by nonlinear differential equations of parabolic type. In the numerical solution of the boundary value problem, the sweep method is used for systems of finite-difference equations. The results of the work of the developed software are presented, as well as the results of computational experiments in graphical form.
Маколада суст утказувчан кат лам билан богланганикки катламли Foeak мухитда газнинг фильтрланиш масаласи математик модели, уни ечишнинг сонли усули ва алгоритми келтирилган.Пастки катлам бир неча турли дебитли кудуклар тизимидан ташкил топган холда ишлайди. Faвaк мухитда газнинг ностационар фильтрланиш жараёни математик модели чизиксиз бир бири билан богланган параболик типли дифференциал тенгламалар тизимибилан ёзилади. Чегаравий масалани сонли ечишда чекли айирмалар тизими учун прогонка усули кулланилада.Чекли айирмалар тизими босим функцияларига нисбатан чизиксиз булгани сабаб, квазилинеаризация усули кулланилиб квазичик тенгламалар тизимига келтирилади. Икки катламли гавак мухитда газларнинг фильтрланиш жараёнини тадкик килиш учун хисоблаш тажрибаларини утказиш максадида масалани ечиш алгоритми ва дастурий таъминот ишлаб чикилган. Дастурий таъминотнинг ишлаши натижалари ва барча хисоблаш тажрибалари натижалари график холда келтирилган.
Modern computer technology creates the opportunity on a qualitatively new basis to solve the problems of designing rational development of gas fields. Modern PCs allow you to take into account, at the stages of designing and analyzing the development of natural gas fields, a variety of natural factors. This, in turn, significantly increases the reliability of the resulting solutions of geological, gas-hydrodynamic and technical-economic problems.When considering issues related to the design, analysis and regulation of the development of multi-layer deposits of natural gases, it is necessary to investigate a large number of options on the PC. Here, the application of methods of mathematical modeling and the theory of computational experiment may prove to be effective. As a result of the computational experiment on a PC, the number of variants under study is substantially reduced.Many problems that have to be solved in the design, analysis and determination of the prospects for the development of gas and gas condensate fields are reduced to the integration of nonlinear differential equations of parabolic type. The necessity to take into account a great variety of geological factors leads to a significant complication of the original differential equations. Often the complexity of differential equations and boundary conditions reaches such a degree that the problems of greatest practical interest can not be solved in analytical form. Therefore, mathematical modeling is increasingly used for such calculations. The application of mathematical modeling for solving problems of underground gas hydrodynamics is based on the mathematical analogy of the flow of filtration processes.The article deals with the mathematical model, methods and algorithms for numerical solution of gas filtration problems in two-porous porous media with the presence of a weakly permeable bridge. In this case, filtration problems are considered two-dimensional and analytical solutions are constructed for certain schematized filtration flows. In addition, information on reservoir properties of the seams necessary for this class of problems has been made much easier. The presence of a gasdynamic connection between the layers is taken into account by the corresponding recording of the differential equations of unsteady gas filtration. A mathematical model of the process of nonstationary gas filtration in a porous medium is described by nonlinear differential equations of parabolic type. In the numerical solution of the boundary value problem, the sweep method is used for systems of finite-difference equations. The results of the work of the developed software are presented, as well as the results of computational experiments in graphical form.